High-resolution angle-resolved photoemission study of CeP: Narrow-band formation of 4f electrons

Article abstract of DOI:10.1103/PhysRevB.55.R3355

High-resolution angle-resolved photoemission spectroscopy at low temperature has been performed on the low-carrier Kondo material CeP. It was found that the p-f bonding state with a dominant 4f character exhibits a finite-energy dispersion of about 40 meV along the ΓX direction in the Brillouin zone. This implies that 4f electrons in CeP form a narrow band owing to the strong anisotropic p-f and d-f mixing.

Full text of DOI:10.1103/PhysRevB.55.R3355

PHYSICAL REVIEW B
VOLUME 55, NUMBER 6
1 FEBRUARY 1997-II
High-resolution angle-resolved photoemission study of CeP:
Narrow-band formation of 4f electrons
H. Kumigashira, S.-H. Yang, T. Yokoya, A. Chainani, T. Takahashi, A. Uesawa, and T. Suzuki
Department of Physics, Tohoku University, Sendai 980-77, Japan
͑Received 8 August 1996; revised manuscript received 15 November 1996͒
High-resolution angle-resolved photoemission spectroscopy at low temperature has been performed on the
low-carrier Kondo material CeP. It was found that the p-f bonding state with a dominant 4f character exhibits
a finite-energy dispersion of about 40 meV along the ⌫X direction in the Brillouin zone. This implies that 4f
electrons in CeP form
a narrow band owing to the strong anisotropic p-f and d-f mixing.
͓S0163-1829͑97͒51306-3͔
Ce compounds have been intensively studied because of
their various intriguing physical properties. The observed
anomalous properties are regarded to originate in the nature
of Ce 4f electrons in the compounds. However, the character
of 4f electrons itself has not been well elucidated and has
been interpreted with either of the two extreme models, lo-
calized and itinerant ones. The single-impurity Anderson
model ͑SIAM͒,1,2 which treats f electrons as localized states,
successfully describes the dense Kondo materials with low-
Kondo temperature3,4 ͑Tk’s͒, while it appears not to work
well for intermediate-valence materials with high Tk’s.5–7
Further, recent photoemission studies on various cerium
compounds8,9 reported the existence of a finite-energy dis-
persion of the ‘‘Kondo-resonance’’ peak at the Fermi level
͑EF͒, suggesting a substantial contribution of lattice effect to
the electronic structure.
spective composition ratio were used as starting materials.
Obtained single crystals were characterized by the x-ray dif-
fraction as well as the resistivity and transversal magnetic
resistance measurements. Measured lattice constant, residual
resistivity at 4.2 K, and magnetoresistivity at 0.8 K ͓⌬%/%͑0͒
where ⌬%ϭ%͑10 T͒-%͑0͔͒ were 5.945 Å, 78 ␮⍀ cm, and 2.7,
respectively, being almost the same values as those of a
single crystal used in the previous de Haas–van Alphen
measurement.17
Photoemission measurements were carried out with a
home-built high-resolution photoemission spectrometer
which has a large hemispherical electron energy analyzer
͑diameter: 300 mm͒ and a highly bright discharge lamp. The
base pressure of the spectrometer was better than 2ϫ10Ϫ11
Torr. The angular and energy resolutions were set at 2° and
50 meV, respectively, for quick data acquisition because of
relatively fast degradation of the sample surface as described
below. A clean mirrorlike surface of CeP ͓100͔ plane was
obtained by in situ cleaving at 15 K just before the mea-
surement and kept at the same temperature throughout the
experiment. Since we observed degradation of the sample
surface as evidenced by increase of background in the spec-
trum after a few hours after cleaving, we recorded every
spectra within one hour. We have measured several samples
and confirmed the reproducibility of the ARPES spectra. The
Fermi level of the sample was referenced to that of a gold
film deposited on the sample substrate and its accuracy was
estimated to be better than 5 meV.
Figure 1 shows ARPES spectra of CeP measured at 15 K
along the ⌫X direction in the fcc Brillouin zone using He I
͓21.2 eV, Fig. 1͑a͔͒ and He II ͓40.8 eV, Fig. 1͑b͔͒ resonance
lines. The intensity of spectra is normalized at a prominent
peak at about 2 eV. The polar angle ͑␪͒ measured from the
surface normal of the cleaved ͓100͔ plane is denoted on each
spectrum. We find in Fig. 1 that ARPES spectra excited by
two different photons ͑He I and He II͒ show remarkably dif-
ferent spectral features; He I spectra have a prominent peak
at about 2 eV while He II spectra exhibit two additional
peaks comparable to the 2-eV peak at about 0.3 and 3 eV,
respectively. In particular, the 0.3-eV peak is remarkably en-
hanced in He II spectra compared with that of He I spectra.
This difference of spectral shape is due to the photon-energy
The p-f mixing model,10 which treats the 4f state as a
band, has successfully explained the experimental results of
semimetallic Ce monopnictides ͑CeX; XϭN to Bi͒.11–17 In
this model two different types of carriers strongly interact
with the Ce 4f state; one is the holelike state originating in
the pnictogen p state located at the ⌫ point in the Brillouin
zone and another is the electronlike state at the X point hav-
ing the Ce 5dt2g character. The d-f mixing between the Ce
4f doublet ͑⌫7͒ and the Ce 5dt2g states, as well as the p-f
mixing ͑the anisotropic hybridization between the Ce 4f
quartet and the pnictogen p3/2 states with the same ⌫8 sym-
metry͒ together play a significant role in characterizing the
observed anomalous properties of Ce monopnictides. Such a
strong anisotropic interaction between the Ce 4f state and
the pnictogen p as well as the Ce 5d state is expected to give
a substantial k ͑wave vector͒ dependence of the hybridiza-
tion strength, resulting in the band formation of the Ce 4f
states. Angle-resolved photoemission spectroscopy ͑ARPES͒
is a unique and powerful experimental technique, providing
directly the E ͑energy͒ -k relation, namely the band struc-
ture. In this paper, we report a high-energy resolution ͑HR͒
ARPES study on single-crystal CeP and discuss the elec-
tronic structure and thereby the validity of the p-f mixing
model.
CeP single crystals were grown in a sealed tungsten cru-
cible using a high-frequency induction furnace. High-purity
Ce ͑99.9% pure͒ and P ͑99.999% pure͒ metals with the re-
0163-1829/97/55͑6͒/3355͑3͒/$10.00
55
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© 1997 The American Physical Society

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H. KUMIGASHIRA et al.
55
FIG. 1. Angle-resolved photoemission spectra of a CeP ͓100͔
FIG. 2. High-resolution angle-resolved photoemission spectra
near EF of CeP ͓100͔ single-crystal surface measured using He II
photons ͑40.8 eV͒. One of the insets shows the fcc Brillouin zone of
CeP projected onto the ͓100͔ plane, together with some representa-
tive ARPES measurement points. The upper inset shows the mea-
sured energy position ͑binding energy͒ of the p-f bonding peak at
about 300 meV as a function of the wave vector along the ⌫X
direction.
single-crystal surface measured along the ⌫X direction in the Bril-
louin zone using the He I ͑21.2 eV͒ ͑a͒ and He II ͑40.8 eV͒ ͑b͒
resonance lines at 15 K. Polar angle ͑␪͒ referred to the surface
normal is indicated on each spectrum.
dependence of the photoionization cross section of atomic
orbitals.18 Since the photoionization cross section of the P 3p
orbital is dominant over those of the other two orbitals ͑Ce
4f and 5d͒ in the He I photon-energy range, the 2-eV peak is
ascribed to the P 3p states. On the other hand, since the
photoionization cross section of the Ce 4f orbital drastically
increases from the He I photon ͑21.2 eV͒ to the He II ͑40.8
eV͒ in comparison with other atomic orbitals ͑P 3p and Ce
5d orbitals͒, the additional two peaks at 0.3 and 3 eV in He II
spectra have a substantial Ce 4f character, especially the
0.3-eV peak which appears to have a dominant Ce 4f char-
acter as is clearly seen from the large enhancement rate from
the He I to the He II excitation.
It is interesting to compare the present result on CeP with
our previous measurements on CeBi.19 It is found from the
comparison of the He I ARPES spectra that the energy bands
with binding energies higher than 1 eV exhibit a similar k
dependence in the two compounds, although the relative in-
tensity of the bands is different between the two. A remark-
able difference in the band structure derived from the He I
ARPES spectra lies near EF ; in CeBi a prominent dispersive
band is observed near EF around the ⌫ point ͑␪ϳ0°͒
͑Ref. 19͒ while in CeP the spectral intensity near EF is con-
siderably reduced and, on the contrary, the intensity is rather
enhanced in the He II measurement, as shown in Fig. 1. This
is explained by the difference in the hybridization strength
between the pnictogen p states and the Ce 4f level. The
stronger p-f hybridization ͑mixing͒ in CeP leads to the in-
crease of Ce 4f character in the bands near EF . Actually, a
small dispersive structure near EF , which may correspond to
the prominent peak in the He I spectrum in CeBi, is observed
in the He II spectrum of CeP ͑shown later͒.
The two peaks observed at 0.3 and 3 eV in the He II
spectra are ascribed to the p-f bonding and antibonding
states, respectively, produced through the many-body corre-
lation effect.20–22 In order to observe a possible dispersive
feature of the bonding peak at 0.3 eV, we measured the He II
spectra near EF with a higher energy resolution ͑50 meV͒
and show them in Fig. 2. One of the insets to Fig. 2 shows
the fcc Brillouin zone projected onto the ͓100͔ plane, to-
gether with some ARPES measurement points. Since it is
established that the electronic states along the high-
symmetry lines in the Brillouin zone make a dominant con-
tribution to an ARPES spectrum because of the lifetime
broadening and the large density of states on the high-
symmetry lines,23 the normal emission ͑␪ϭ0°͒ spectrum re-
flects the electronic structure mainly at both ⌫ and X points
while the ARPES spectrum at ␪ϭ20° corresponds to the X
point as shown in the inset. In Fig. 2, we clearly find a small
but definite energy dispersion of the bonding peak from the
⌫͑X͒ point ͑␪ϭ0°͒ to the X point ͑␪ϭ20°͒. Another inset to
Fig. 2 shows the measured binding energy of the bonding
peak as a function of the wave vector along the ⌫X direction.
The peak of bonding states is located at about 290 meV at
the ⌫͑X͒ point, starts to move away from EF to the high
binding energy with increasing polar angle ͑␪͒, turns around
at ␪ϭ15°, and moves back to the low binding energy till
␪ϭ20°. The magnitude of total energy dispersion is about 40

55
HIGH-RESOLUTION ANGLE-RESOLVED . . .
R3357
meV. We find that the observed energy dispersion matches
the crystal periodicity, as is evident by the symmetric behav-
ior both at the ⌫͑X͒ point ͑␪ϭ0°͒ and the X point ͑␪ϭ20°͒.
This indicates that the observed energy dispersion is of an
intrinsic bulk origin. Considering the strong Ce 4f character
of the band, it is inferred that Ce 4f electrons in CeP form a
narrow band having the energy dispersion of about 40 meV.
The observed energy dispersion shows a good accordance
with the prediction by the p-f mixing model.10 The p-f mix-
ing model explains that the finite-energy dispersion of Ce 4f
electrons is produced through the anisotropic p-f mixing
around the ⌫ point and the interatomic d-f mixing at the X
point. Actually, a small shoulder near EF in the ARPES
spectrum of ␪ϭ0° may represent the hole pocket, as has been
suggested in the ARPES study on CeBi.19 A quantitative
comparison of the energy dispersion of the Ce 4f band be-
tween the present ARPES results and the band calculation
based on the p-f mixing model would give a deeper insight
into the hybridization strength between the Ce 4f states and
the P 3p and Ce 5d states. However, at the present stage, the
calculation10 treats the many-body effect as one effective f
level and approximates the self-energy using a mean field. A
more realistic band calculation based on the p-f mixing
model including two f levels is necessary to be compared
with the present ARPES results.
In conclusion, we have performed a high-resolution
angle-resolved photoemission spectroscopy ͑HR-ARPES͒ on
single crystal CeP. The He I ͑21.2 eV͒ spectrum shows a
prominent peak at 2 eV while the He II ͑40.8 eV͒ spectrum
exhibits two additional peaks comparable to the 2-eV peak at
0.3 and 3 eV. By considering the photoionization cross sec-
tion of each atomic orbital, the 2-eV peak is assigned to the
P 3p states while the 0.3- and 3-eV peaks are ascribed to the
p-f bonding and antibonding states, respectively, with a
dominant Ce 4f character. HR-ARPES measurements near
EF showed that the bonding peak has a small but definite
͑about 40 meV͒ energy dispersion matching well the crystal
periodicity. This suggests that Ce 4f electrons in CeP form a
narrow band through the anisotropic p-f and d-f many-body
interaction.
We are very grateful to Professor O. Sakai for many use-
ful discussions. T.Y. and A.C. thank the Japan Society for
the Promotion of Science for financial support. This work
was supported by grants from the NEDO and the Ministry of
Education, Science and Culture of Japan.
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